Thermal modelling of parabolic trough collectors - Solar Energy Sciences and Engineering Applications - page 179

the following Nusselt number correlation developed by Gnielinski (1976) is used for
the convective heat transfer from the receiver pipe to the HTF:

f pi / 8 Re D pi − 1000 Pr f

Pr f
Pr pi

0 . 11

Nu D pi =

12 . 7 f pi / 8 Pr 2 / 3
f

1

1 + −

10 6 For 0 . 5 < Pr f < 2000 and 2300 < ReD pi < 5 × (6.2.8)

with

= 1 . 82 log (Re D pi ) 1 . 64 − 2

f pi − (6.2.9)

where: f pi = friction factor for the inside surface of the receiver pipe, D pi ;Pr f = Prandtl

number evaluated at the HTF temperature, T f ; and Pr pi = Prandtl number evaluated

at the receiver pipe inside surface temperature, T pi .
Except for Pr pi , all fluid properties are evaluated at the mean HTF temperature,
T f . The correlation assumes that the receiver pipe has a smooth inside surface and that
the heat flux and temperature are uniform.
The above equations are valid for both turbulent pipe flow and the transitional
flow which occur for Reynolds numbers between 2300 and 4000 (Cengel, 2006).
Furthermore, the above correlations are adjusted for fluid property variations between
the receiver pipe wall temperature and the bulk fluid temperature. The program will
display a warning message if the correlation is used out of the range of validity, shown
in Equation 6.2.8.

6.2.2 Conduction heat transfer through the receiver pipe wall
Conduction heat transfer through the receiver pipe wall is determined by Fourier's law
of conduction through a hollow cylinder (Cengel, 2006) given by:

2 π k pipe T pi − T po

ln D po
D pi

q pi-po,cond = (6.2.10)

where: k pipe = receiver pipe thermal conductivity at the average receiver pipe tem-

T po )/2 (W/m- ◦ C); T pi receiver pipe inside surface temperature ( ◦ C);

perature (T pi + =

receiver pipe outside surface temperature ( ◦ C); D pi

T po = = receiver pipe inside diame-

ter (m); and D po receiver pipe outside diameter (m).

In this equation the thermal conductivity is considered as constant, and evaluated
at the average temperature between the inside and outside receiver pipe surfaces.
The thermal conductivity depends on the receiver pipe material type. The receiver
performance model includes one copper and three types of stainless steels (304L, 316L,
and 321H), which can be chosen by the user at the beginning. If copper is chosen, the
thermal conductivity is constant and equal to 385 W/m- ◦ C. If stainless steel 304L or
316L is chosen, the thermal conductivity is calculated from:

=

k pipe = (0 . 013)T pi-po + 15 . 2 (6.2.11)